A key feature of complex systems is that their behaviour can vary significantly
depending on their location in parameter space. A major challenge
for researchers is to understand how combinations of system parameters
influence behaviour; that is, to understand the shape of parameter space.
Tools for visualising the structure and dynamics of complex systems and the
shape of their parameter spaces play an important role in addressing this
challenge. Many of these tools are developed to address problems in specific
domains. If complex systems share certain general properties that transcend
their specific domain, it should be possible to share tools for understanding
these systems between domains. One technique that has been proposed for
achieving this is the use of design patterns (Wiles and Watson, 2005).

Patterns are a tool that enables the collective knowledge of a particular
community to be recorded and transmitted in an efficient manner. Initially
developed in the field of architecture and later developed by software engineers
(Gamma et al., 1995), they have now been adopted by the complex systems
modelling community (Wiles and Watson, 2005). It can be argued that,
while most complex systems models are idiosyncratic and highly specific to
the task for which they are constructed, certain tools and methodologies
may be abstracted to a level at which they are more generally applicable.

This report describes two patterns – the Recursive Parameter pattern
(Section 1) and the Interactive Heatmap pattern (Section 2) – that provide
techniques for managing the exploration and visualisation of large parameter
spaces. These patterns are based on research reported in (Geard, 2006)
and a visualisation tool that implements these patterns (in the context of
exploring the parameter space of developmental genetic systems) is available
from http://www.itee.uq.edu.au/~nic/_linmap.